It is difficult to produce a 2-dimensional image of a relatively deep 3-dimensional scene in which both relatively close and relatively distant objects within the scene appear in focus. For example, when a microscope is used to photograph a 3-dimensional specimen, portions of the specimen that are not in or near the focal plane are blurred or invisible.
Adelson in U.S. Pat. No. 4,661,986 (incorporated herein by reference) teaches a method for obtaining a focused 2-dimensional image from an assemblage of M separately focused 2-dimensional images of the same 3-dimensional scene. Adelson employs an image processing algorithm developed by Dr. Peter J. Burt (hereinafter referred to as the Burt Pyramid). Adelson's method separately analyzes each of the M separately focused images into N similar sets of pixel samples. The method then selects, on a pixel-by-pixel basis from each group of M corresponding sets of the assemblage, the best focused pixels, to derive a single analyzed image of N sets of improved-focus pixels. By employing the Burt Pyramid image synthesizing technique, Adelson synthesizes the final 2-dimensional image from the single analyzed image of N sets.
Adelson describes the selection of image pyramid coefficients from a collection of source image pyramids by taking those of maximum squared value or maximum absolute value, or by other methods that depend on the relative coefficient values themselves. Adelson thus constructs a pyramid transform for each source image. At each pyramid sample position, corresponding samples of each sub-group are selected. All the selected sub-groups are combined to form a single pyramid representing the composite image. The composite image is recovered through an inverse Burt pyramid transform.
The Burt pyramid transform of the improved-focus two-dimensional image is assembled octave by octave, choosing the corresponding octave of the original image having the highest intensity level. The improved-focus two-dimensional image is then generated from its Burt pyramid transform by performing an inverse pyramid transform procedure. A bibliography of the early literature concerning the Burt pyramid transform may be found in U.S. Pat. No. 4,661,986.
The Burt pyramid may be viewed as a set of low-pass or band-pass filtered copies of an original image in which both the band limit and the sample density are reduced in regular steps. Pyramid construction is outlined in FIG. 1. The process begins with the formation of a low-pass filter or Gaussian pyramid through the steps shown on the top row of FIG. 1. The original image, or source image, is designated as G(0). This original image, G(0), is first low-pass filtered (F1) then subsampled by a factor of two in the vertical and horizontal directions (F2) to obtain an image G(1), which is half as large in each dimension as G(0). G(1) is then filtered and subsampled in the same way to obtain G(2). These steps are iterated to generate the tapering sequence of images which constitute levels of the pyramid. Since both resolution and image size are decreased, the formation of the various levels of the Gaussian pyramid may be referred to as filtering and decimating steps. With each level of the pyramid, the bandwidth is reduced by one octave step.
The Gaussian pyramid is a set of low-pass filtered images. In order to obtain band-pass images, each level of the Gaussian pyramid may be subtracted from the next lowest level, as shown in the bottom row of FIG. 1. Because these arrays differ in sample density, it is necessary to interpolate new samples between those of a given array before it is subtracted from the next lowest array. As shown, the Laplacian, for example L(0), is formed by restoring the subsampled data from G(1), for example (by inserting zero-valued samples between the given samples (F2') then applying an interpolation filter (F1')) and subtracting the data from the G(0) Gaussian. The Laplacian formed this way is known as the reduce-expand Laplacian. Alternatively, the Laplacian may be formed without subsampling and re-interpolation, as shown by the dotted line in FIG. 1. This is known as a filter-subtract-decimate Laplacian. Thus, the Laplacian is a sequence of band-pass images L(0), L(1), L(2), etc. This is precisely how Adelson separates the visual frequencies of each source image into eight ranges.